1. Technical Field
This disclosure relates generally to oil and gas well logging, and more specifically to directional resistivity measurements using a transmitter/receiver pair whereby there is relative rotation between the transmitter and receiver antennas. A method is disclosed for mathematically extracting some or all of the nine components of the electromagnetic coupling tensor for a formation and the distances to bed boundaries using the transmitter/receiver pair described herein.
2. Description of the Related Art
An alternative to wireline logging techniques is the collection of data on downhole conditions during the drilling process. By collecting and processing such information during the drilling process, the driller can modify or correct key steps of the operation to optimize performance. Schemes for collecting data of downhole conditions and movement of the drilling assembly during the drilling operation are known as measurement-while-drilling (“MWD”). Similar techniques focusing more on measurement of formation parameters than on movement of the drilling assembly are known as logging-while-drilling (“LWD”). However, the terms MWD and LWD are often used interchangeably, and the use of either term in this disclosure will be understood to include both the collection of formation and borehole information, as well as data on movement and placement of the drilling assembly. The term “parameter”, as used herein, includes, but is not limited to, formation properties, dip and azimuth of bed boundaries, distances to bed boundaries, as well as data on movement and placement of the drilling assembly. Formation “properties” include, for example, vertical resisitvity, horizontal resistivity, the conductivity tensor, the dielectric permittivity, porosity, and saturation. MWD tools are available to guide drill strings and therefore the resulting boreholes into more productive reservoir zones. MWD tools used for this purpose typically have been propagation resistivity tools, also known as array compensated resistivity (ARC) tools, with a 360° measurement and deep imaging capability to detect fluid contacts and formation changes up to 15 feet from the borehole. Measurements are commonly made of the phase-shift and attenuation of the signals at the receiver coils, which are indicative of the rock conductivity.
Currently available ARC tools are non-azimuthal and utilize two receivers that compensate for any electronic drift associated with the transmitter. The electronic drift associated with the two receivers and any imbalance between the two receivers is removed using a scheme called borehole compensation, which involves the use of a second transmitter, symmetrically placed with respect to the first transmitter. The transmitters are alternately energized so two phase difference signals can be measured when the two transmitter coils operate at identical frequencies. However, alternately using two transmitter coils slows the rate of data acquisition, which can lead to errors due to the time delay between sequential measurements. Further, use of multiple transmitters may require the signals to be time-multiplexed when operating at the same frequency to avoid cross-talk. Multiplexing slows the rate of data acquisition. The errors due to time delays are magnified when drilling rates (rate of penetration) are high.
As an improvement to the ARC tools, tools were developed that incorporate tilted receiver antennas in the drill collar. The non-axial antennae obtain directional electromagnetic measurements that are used to determine distance and azimuthal orientation of formation boundaries in any type of mud. These measurements are transmitted uphole and are displayed on a graphical interface to provide information on distance to boundaries, formation resistivity and orientation. This information is critical in low resistivity pay zones and in laminated formations because accurate identification and characterization of hydrocarbon reserves is not possible without knowing the resistivity anisotropy. Further, using a transmitter/receiver pair in which one of the antennae is tilted or non-axial, a ratio of any two measurements at two different azimuthal angles can be used to remove the electronic drift of both the transmitter and receiver.
However, if the resistivity anisotropy of the formation is to be completely understood, values for all nine components of the electromagnetic coupling tensor need to be obtained. For example, a complex conductivity matrix can be expressed as
      σ    apparent    =      (                                        σ            xx                                                σ            xy                                                σ            xz                                                            σ            yx                                                σ            yy                                                σ            zx                                                            σ            zx                                                σ            zy                                                σ            zz                                )  which can be inverted for horizontal resistivity, vertical resistivity, dip angle and azimuth assuming a dipping layered earth model.
Further, methods for extracting all nine components (XX, XY, XZ, YX, YY, YZ, ZX, ZY, ZZ) of the electromagnetic tensor are available for tri-axial wireline tools that are commonly referred to as tri-axial measurements. This method preferably uses three collocated transmitters and three collocated receivers with orientations in the x, y and z directions wherein the z direction is along the tool axis or coaxial with the tool. Measurements with different transmitter/receiver (T/R) combinations that are corrected for antenna magnetic dipoles yield the nine coupling tensor components directly. Obviously, the use of three transmitters and three receivers (i.e., six antennas) presents data acquisition and gain correction problems.
Returning to MWD and LWD tools, Schlumberger's PERISCOPE™ tool uses tilted and axial antennas and the rotation of the tool or drill string to obtain the five non-zero components when in planar or “layer cake” formations using a fitting algorithm performed on harmonic behavior of the measurement with respect to the tool face. A tool having three transmitters with different azimuthal orientations and a tilted receiver can, in combination with tool rotation, obtain all nine components of the electromagnetic coupling tensor.
Therefore, using current technology, determination of all nine couplings (XX, XY, XZ, YX, YY, YZ, ZX, ZY, ZZ) of a formation electromagnetic coupling tensor requires a minimum of four antennas (one tilted antenna and three possibly collocated antennas) combined with the tool rotation. The relative gain of each antenna pair needs to be either measured or estimated from the data. Also, the azimuthal angle of all respective antenna combinations must be measured and considered constant, which may detract from the accuracy of the calculations.
Therefore, there is a need for a tool and method that provide for a more simplified extraction of all nine components of the electromagnetic coupling tensor which avoids the use of multiple transmitters and receivers and the inherent disadvantages associated with multiple transmitter/receiver use.